Enhanced capability of model fitting to nuclear level density and heat capacity: testing on ⁹³⁻⁹⁸Mo nuclei

We propose an improved fitting approach that improves reliability in studying the nuclear level density (NLD) and thermodynamic quantities. The proposed method, which relies on the fact that experimental fluctuations or outliers, if they exist, should not be involved in the fitting process, is validated with a set of data artificially generated with anomalous data points being intentionally inserted. In order to showcase the advantages of the proposed technique, we have applied it to re-investigate the back-shifted Fermi gas (BSFG) level density parameters and thermodynamic quantities, particularly the heat capacities, of ⁹³⁻⁹⁸Mo isotopes. We have found that the range of values for the level density parameter of ⁹³Mo (approximately from $8.5$ to $9.0$ MeV⁻¹) is notably smaller compared to that obtained for the other isotopes of Mo (approximately from $10.5$ to $11.5$ MeV⁻¹). This observation is different from previous predictions, in which the values of level density parameter of all Mo isotopes are in the same range. This is because among the Mo isotopes under examination, ⁹³Mo ($N = 51$ neutrons) has the smallest number of valence neutrons, namely only a single neutron away from the closed $N = 50$ shell. In addition, thanks to the proposed method, we have discussed the effects of data fluctuations on the BSFG NLDs and thermodynamic quantities of ⁹³⁻⁹⁸Mo isotopes, from which our recommendation for future works is announced. On top of that, we should notice that the proposed approach can be further applied to any work involving the fitting of a phenomenological model to empirical data.